reserve k,m,n for Nat,
  a, b, c for object,
  x, y, X, Y, Z for set,
  D for non empty set;
reserve p, q, r, s, t, u, v for FinSequence;
reserve P, Q, R, P1, P2, Q1, Q2, R1, R2 for FinSequence-membered set;
reserve S, T for non empty FinSequence-membered set;

theorem
  for P, Q st Q c= P* holds Q* c= P*
proof
  let P, Q;
  assume A1: Q c= P*;
  let a;
  assume a in Q*;
  then consider n such that A2: a in Q^^n by Th5;
  Q^^n c= P* by Th14, A1;
  hence thesis by A2;
end;
